Reducing molecular electronic Hamiltonian simulation cost for linear combination of unitaries approaches

Abstract We consider different linear combination of unitaries (LCU) decompositions for molecular electronic structure Hamiltonians. Using these LCU Hamiltonian simulation on a quantum computer, the main figure merit is 1-norm their coefficients, which associated with circuit complexity. It derived that lowest possible given half its spectral range. This norm decomposition practically unattainable general Hamiltonians; therefore, multiple practical techniques to generate are proposed and assessed. A technique using symmetries reduce further also introduced. In addition considering in Schrödinger picture, we extend it interaction substantially reduces 1-norm.